Authors: Julie E. Czerneda
ReVISIONS (15 page)
Without knowing the rules of algebra, it is impossible for character to be established.
Without logarithmic scales, it is impossible to conserve paper.
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Achilles and the Tortoise: The Second Heat
SOCRATES: I went down yesterday to the Piraeus with Glaucon the son of Ariston, that I might offer up my prayers to the goddess; and also because I wanted to see how the city would celebrate the festival. I was delighted with many of the events, particularly the sports competitions. But then that old madman Zeno showed up and began to rant loudly to his neighbors during the races.
POLEMARCHUS: No doubt he declaimed his paradox?
S: Can he speak of anything else?
THRASYMACHUS: What paradox is this?
P: Zeno pictures a race between the swift Achilles and a tortoise, in which the tortoise is given a head start of perhaps ten paces.
T: Unless the race length is ten paces and the width of a fingernail, Achilles would surely win.
P: Zeno contends otherwise. For before Achilles can close the ten-pace gap, he must run the first five paces. And before he can close the remaining five-pace gap, he must run the first half of that: two and a half paces. And before he can close the remaining two and a half paces, he must run the first half of that distance, too. You see the pattern?
T: Yes, certainly.
P: Therefore Zeno says Achilles must run an infinite number of these half-distance races; and although each such race is half the distance of the previous, yet there are still an uncountable number of them. How can a man run an infinite number of races in a finite lifetime? Zeno claims Achilles will never catch up with the tortoise, and moreover that all movement is impossible.
T: I do not agree with Zeno's conclusion though I see no error in his argument. Socrates, can you help me resolve the dilemma?
S: Zeno's error is simple. He assumes that distance is infinitely divisible but will not grant a similar favor to time. For suppose swift Achilles can run ten paces in a single heartbeat. Then he runs the first five paces in half a heartbeat; he runs the next fraction of the race in a quarter of a heartbeat; he runs the next in an eighth of a heartbeat; and so on. Achilles therefore has an infinite number of ever-smaller time segments to run an infinite number of ever-smaller distance segments. In the limit, as the distance segments D go to zero, the time segments
T also go to zero. Therefore there is no paradox.
P: Yet what of Achilles' speed? For speed is distance divided by time . . . and if both D and T go to zero, do we not have a case of zero divided by zero? You must realize, Socrates, that in Athens, advocating division by zero is a crime punishable by death. Do you wish to corrupt our youth with seditions against the very foundations of mathematical discourse?
S: I preach no seditions. My Socratic method is merely to slice ever more finely until I arrive at the truth. Do you realize my techniques can analyze all manner of phenomena? The fall of an apple. The movements of stars and planets. Why bubbles are round and how to calculate pi.
P: None of that matters, Socratesânot if you divide by zero! Such talk offends the gods. I beg you, abandon these notions. Do you wish to be executed? [Silence.]
S [stiffly]: I do not divide by zero itself. Merely by values approaching zero.
P: That is an extremely delicate distinction, Socrates . . . and I am afraid the elders of Athens will not be able to differentiate.
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The Death of Ideals (by Plato)
My mentor Socrates is dead. Compelled to take poison because his ideas transgressed the status quo.
Never mind that Athens pretends to venerate ideas. Our ambassadors have traveled the entire worldâto Persia, the Indus, the court of the Chou emperor, and everywhere in betweenâdeliberately seeking out systems of thought, to make our city a paragon of wisdom.
Yet we are incapable of honoring one of our own.
Now Socrates is dead. His writings have been destroyed. His knowledge is lostâhis vast vast knowledge. For the notions that led to his death were infinitesimal compared to the greater body of work he never made public. The secrets known only to his most intimate students.
Those who loved him.
Like me.
I watched him die. I saw the best mind of my generation destroyed by intolerance, called heretical, stripped naked, dragged through the hemlock streets at dawn by angry fanatics.
An agile-headed trickster burning with an ancient Zoroastrian grasp of the fiery calculus running the machinery of night.
Who bared his brain to Heaven under the Parthenon and heard algebraic angels totaling Buddhist zeros into infinite chanted sums.
Who got arrested in pubescent years returning through Sparta with a contraband copy of Lao Tzu under his robe.
Who studied Aesop, Mahavira, Pythagoras, and fourteen forbidden Upanishads to find the cosmos instinctively ordering itself in probabilistic sample spaces.
Who read Daniel's writing on the wall, walked with saints and angels in the Babylonian furnace, slept in the lions' den, slept with all the lions, triangulated their manes to five decimals.
Who wept at his first glimpse of analytic geometry, wept copiously asymptotically exponentially logarithmically, all the while on his way to becoming a superior man.
Who took T to zero in the company of epsilon and delta, then worked backward as infinite Σ became smoothed-out, and slopes reversed themselves into areas-under-the-curve always always plus a constant or marks would be deducted.
Who journeyed to Athens, who differentiated in Athens, who came back to Athens & integrated in vain, who factored over Athens & X-the-unknowned in Athens and finally went away to take Athens' measure, & now Athens is lonesome for her hero.
Who dreamed and made incarnate more secret things still: the transfinite aleph, the rank-clashing matrix transforms, the groups and the rings and the prime-power fields, the stretched deformations of bourgeois space into patchy coordinate manifolds, the torn topologies, the random walks, the bloom of cardinalities, series and sequences, the functors, the metrics, the lemmas, the postulates, the perfect perfections of perfected forms, now with the absolute magnitude of the poem of mathematics butchered in Socrates' body, gone and dead for the next two thousand years.
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Light. Dark. Light. Then fire.
Light. Dark. Light. And fire.
Light. Dark. Light. Ahh, fire!
Fire is light. And fire, it burns. Burns the dark.
Fan . . . the . . . flames!
Revision Point
As noted at the beginning of the story, the Axial Age (600-400 BCE) was a sort of Renaissance wherein many old tribal beliefs were questioned and replaced. Throughout Europe and Asia, several generations of thinkers tried to make sense of the world in a way that had never been tried before. As a result, the Axial Age saw the birth of Zoroastrianism (the first religion that combined true monotheism with a strong belief in an afterlife), Buddhism, Taoism, Confucianism, Jainism, and modern Hinduism, as well as the late Jewish prophets and the most important Greek philosophers. The religions and philosophies created during this time set Eurasia's intellectual agenda for more than two thousand years.
What the Axial Age
didn't
give us was much advancement in science. A few small steps were taken, but nothing comparable to the great developments in philosophical thought. Why not? Perhaps because it was still the Bronze Age, and humanity hadn't yet invented useful things like telescopes, mechanical clocks, sextants, etc. People could think, but they couldn't
measure
. What kind of science could flourish in such an environment?
didn't
give us was much advancement in science. A few small steps were taken, but nothing comparable to the great developments in philosophical thought. Why not? Perhaps because it was still the Bronze Age, and humanity hadn't yet invented useful things like telescopes, mechanical clocks, sextants, etc. People could think, but they couldn't
measure
. What kind of science could flourish in such an environment?
Well, there's one realm of science where abstract brainpower is all that counts: math. It occurred to me that if all those prophets and philosophers had just spent a little time putting their ideas into mathematical form, the Axial Age would have been a lot more fun . . . at least to a math geek like myself. Therefore, I've attributed the invention of various mathematical concepts (from positive and negative numbers, up to calculus and beyond) to appropriate thinkers of the Axial Age. It's scary just how easily the math and the people lined up. . . .
J.A.G.
THE TERMINAL SOLUTION
by Robin Wayne Bailey
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N the matter before us which now threatens us so direly we have relatively few facts, and the hypotheses and opinions we now offer are subject to so many caveats and arguments as to invite ridicule not just from numerous of our fellow colleagues, most notably Dr. Joseph Lister of the King's College Hospital and in Paris M. Louis Pasteur, but from clergy and from political circles throughout the empire as well.
N the matter before us which now threatens us so direly we have relatively few facts, and the hypotheses and opinions we now offer are subject to so many caveats and arguments as to invite ridicule not just from numerous of our fellow colleagues, most notably Dr. Joseph Lister of the King's College Hospital and in Paris M. Louis Pasteur, but from clergy and from political circles throughout the empire as well.
Nevertheless, the facts are the facts, and I take no great pleasure in noting that the British Medical Association as well as leading figures within the Royal College of Surgeons, if somewhat slowlyâindeed, and without leveling judgments, I might say too slowlyâhave come to concur with much of what I now report.
We can state as fact that the epidemic which now confounds and menaces us had its origins in the darkest heart of Africa, perhaps somewhere along the Ruvuma River or along the banks of the great lakes of Mweru and Bangweulu. It is impossible to more precisely determine where it first appeared. As fearful as this disease is to us, it has struck a far more devastating blow there. Many of the key settlements and villages where important clues might have been found are now either abandoned or completely wiped out. Ujiji and Kolobang were burned. Capetown has completely quarantined itself.
We know as fact, however, that the renowned explorer and writer, David Livingstone was already quite ill when he returned to London on July 23, 1864. His physician, one Doctor Samuel Overton, diagnosed his several maladies as symptomatic of malaria, and there can be no doubt that malaria was present. However, Doctor Overton also indicated the occurrence of several purplish lesions of an unknown and possibly cancerous nature upon Livingstone's torso. These lesions seemed to defy all treatment.
So, detracting no honor from his famous name, it is with David Livingstone that we find the first evidence of this plague, which I now call African Invasive Disease, upon our shores. And it is with David Livingstone that we begin to document a curious and notable progression of subsequent, and I might add inevitably fatal, occurrences. Most immediate among these are Dr. Overton, himself, and a number of his patients. Overton's copious notes describing his own symptoms and pathology provided useful groundwork for my investigations.
From this point, I must speak with some delicacy about matters that may shock or offend, for in charting the progress of this plague. . . .
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Dr. Joseph Bell laid his pen aside, leaned his elbows on his writing table, and in the dim, yellowish light from a single gas lamp, rubbed his eyes. In his mind, he'd gone over this passage a dozen times and on paper at least half that many. He felt tired, so very deeply tired. The summary of his investigations at which he was working and which he would soon present to the British College of Physicians was proving difficult, requiring wording that was foreign to his blunt nature.
“Devil damn us all!” he grumbled, wadding his pages up and hurling them across the room of his cluttered apartment. He stared in disgust after the parchment ball as it bounced off a bookcase full of medical texts and settled into a shadowy corner. Then, recovering from his outburst, he settled back in his chair and rubbed his eyes a second time as he muttered to himself, “Indeed, he already hasâdamned us every bloody one.”
Weary to the bone, he tried to push all thought from his mind. He knew he needed sleep, but there was no time for that. There were riots in Whitechapel, in Aldgate, and Spitalfields, demonstrations at the gates of Buckingham, itself.
He squeezed his temples as he rose and paced back and forth over the carpet which Mrs. Hudson, his housekeeper, had once kept so clean. Poor, sweet woman. She was dead, too, like so many others.
On the corner of his desk rested a small black case, and in it his hypodermic needle. Beside that, the cocaine bottle. In that vial of cobalt blue he might find a little rest. He ran his fingers over the case, a fingertip over the bottle's lid, feeling the hunger gnawing inside him. He pushed both farther back on the desk where the light didn't reach and where the little glass bottle didn't sparkle quite so interestingly. Perhaps later, but there was still so much to do.
Downstairs, the front door closed softly, but not so softly as to escape his hearing. Nudging back the edge of a lace drapery (more of Mrs. Hudson's handiwork), he peered down to watch a thin figure in top hat and black cloak descend the three stone steps and move with a quickly furtive gait into the damp, fogenshrouded street. The silver head of a walking stick which he tucked under one arm flashed briefly.
A moment later, footsteps sounded on the seventeen steps that led from the first floor, where he and his assistant maintained medical offices, to the upper rooms which they shared in these troubled times. The door's brass knob turned. The door opened. Dr. Arthur Doyle, tall and slender, dark of hair, not yet thirty, stepped from the brighter hallway into the gloom of their living quarters. He closed the door in a thoughtful manner and leaned back against it. His slim-fingered hand lingered on the knob.
At Edinburgh University Hospital, Doyle had been Bell's finest student. His mind was keen, and Bell had quickly taken him on as a clerk. Now a doctor fully in his own right, he continued to work loyally at Bell's side.
“Even in this weak light,” Bell commented as he settled into an overstuffed chair near the window and regarded the younger doctor, “you look quite ashen.”
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